Solutions of the problems and riders proposed in the Senate-house examination for 1854, by the moderators and examiners |
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Side 11
... axes of a rigid body , and shew that for every point in space there exists a system of such axes . Shew that in general there is only one point for which the principal axes are parallel to those drawn through a given point ; but that ...
... axes of a rigid body , and shew that for every point in space there exists a system of such axes . Shew that in general there is only one point for which the principal axes are parallel to those drawn through a given point ; but that ...
Side 23
... axes , is z = x cota + y cotß = px + qy ; therefore the volume of the part between OBDA and OFGE SS ρα = [ " [ [ z dy dx = [ " [ " ( px + qy ) dy dx a2b ab2 = P +9 2 = ab 2 2 ( ap + bq ) . And since this is always the smaller part , the ...
... axes , is z = x cota + y cotß = px + qy ; therefore the volume of the part between OBDA and OFGE SS ρα = [ " [ [ z dy dx = [ " [ " ( px + qy ) dy dx a2b ab2 = P +9 2 = ab 2 2 ( ap + bq ) . And since this is always the smaller part , the ...
Side 24
... axes are a , b , the greatest value of ጥ r ' is equal to 3 / a 26 ( 0-0 ) a dx ' dy We know that · ( 1 ) , dy ' da and therefore , by differentiation , d'x'.dy ' - d'y'.dx ' dy ' dx d'y - dy d'x dx2 1 Hence = ' 2 ( dx'd'y ' - dy'd'x ...
... axes are a , b , the greatest value of ጥ r ' is equal to 3 / a 26 ( 0-0 ) a dx ' dy We know that · ( 1 ) , dy ' da and therefore , by differentiation , d'x'.dy ' - d'y'.dx ' dy ' dx d'y - dy d'x dx2 1 Hence = ' 2 ( dx'd'y ' - dy'd'x ...
Side 29
... axes are half the semi - latus - rectum , and half the minor axis of the given ellipse ; therefore the locus of G is an ellipse whose semi - axes are one- fourth of the semi - axis minor , and one - fourth of the semi - latus- rectum of ...
... axes are half the semi - latus - rectum , and half the minor axis of the given ellipse ; therefore the locus of G is an ellipse whose semi - axes are one- fourth of the semi - axis minor , and one - fourth of the semi - latus- rectum of ...
Side 31
... axes 4a , 46. The latter belongs to the case when the triangle is constantly zero . 11. The radii vectores of any series of points in the path of a particle , moving about a centre of force , being in arith- metical progression , the ...
... axes 4a , 46. The latter belongs to the case when the triangle is constantly zero . 11. The radii vectores of any series of points in the path of a particle , moving about a centre of force , being in arith- metical progression , the ...
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Solutions of the Problems and Riders Proposed in the Senate-House ... Exam Papers Cambridge Univ Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
angular velocity asymptote axes Cambridge catenary centre of force centre of gravity chord circle cloth conic section constant cos² cose cosẞ cota cotß Crown 8vo curvature curve cylinder denoting described diameter direction distance dx dy dy dx ecliptic elastic ellipse equal equation equilibrium Fellow of St fixed point fluid geometrical progression given Hence horizontal hyperbola inclined plane intersection lamina latus rectum length locus longitude M.A. Fellow major axis middle point motion orbit parabola parallel particle passing perpendicular position pressure projection prove radius refraction right angles ring shew sides Similarly sine sino sinẞ straight line string Supposing surface tana tangent tanß triangle Trinity College tube V₁ vertical
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Side 214 - For really ripe scholarship. extensive acquaintance with Latin literature, and familiar knowledge of continental criticism, ancient and modern, it is unsurpassed among English editions.
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Side 167 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
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Side 209 - ANTHOLOGIA Latina Selecta. In 2 vols. Small 8vo. VOL. I.— Containing select Epigrams of Catullus, Virgil, Claudian, Ausonius, with others from the Anthologia Latina.
Side 167 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.